Remark 1

Tag 0C01, permanent. Cite it as [Bourbaki, Tag 0C01].

General Topology, chapter VIII, § 1. Complex numbers, quaternions

With the use of the relations $\|x + y\| = \|x\| + \|y\|$ and $\|xy\| = \|x\|\cdot\|y\|$ it can be proved directly, as with the field of complex numbers in no. 2, that the topology of $\mathbf{R}^4$ is compatible with the division ring structure of $H$ (cf. Chapter IX, § 3, no. 2).

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

Chapter IX, § 3, no. 2